Stress Testing Trading Desks

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1 Stress Testing Trading Desks Michael Sullivan Office of the Comptroller of the Currency Paper presented at the Expert Forum on Advanced Techniques on Stress Testing: Applications for Supervisors Hosted by the International Monetary Fund Washington, DC May 2-3, 2006 The views expressed in this paper are those of the author(s) only, and the presence of them, or of links to them, on the IMF website does not imply that the IMF, its Executive Board, or its management endorses or shares the views expressed in the paper.

2-3, 2006 The views expressed in this paper are those of the author(s) only, and the presence of them, or of links to them, on

2 Comptroller of the Currency Administrator of National Banks Stress Testing Trading Desks IMF May 2, 2006 Michael Sullivan Deputy Director Risk Analysis Division Washington, DC

2, 2006 Michael Sullivan Deputy Director Risk

3 Comptroller of the Currency Administrator of National Banks Disclaimer Personal opinions of the author and not of the Treasury Department, the OCC, or RAD

4 Supervision Strategy for Trading Desks: The role of stress testing MRR requires appropriate stress tests Compliance evaluated at 2 levels 1. Trading desk/line of business Focus on stress tests for desk or business unit 2. Market Risk Management function Focus on stress tests across trading desks In each case: stress testing considered along with other aspects of trading desk management and controls, including market risk management

Trading desk/line of business Focus on stress tests for desk or business unit 2.

5 Basics A stress test: Measures performance under plausible extreme adverse conditions. Elements of a stress test Define performance measure Determine affected positions Decide on scenario of changes in market conditions Estimate impact on performance Purpose: Aggregate exposure across positions or desks Identify risk exposure not captured by other measures Limit stress exposure reflecting mgmt tolerance

of changes in market conditions Estimate impact on performance Purpose: Aggregate exposure across

6 Example 1. Relation to VaR Stress test result set to worst case in historical simulation VaR Advantages Stress scenario determined by vulnerability of positions Stress test results in loss Reflects historical pattern of comovement of risk factors (plausible) Disadvantages Inherits limitations of VaR measure, esp. approximate mapping of scenario to P/L Actual scenarios may be complicated, subtle Reflects historical pattern of comovements of risk factors (extreme?)

determined by vulnerability of positions Stress test results in loss Reflects historical pattern of comovement of

7 Correlation vs. Comovement Connection: correlation = average linear comovement A criticism of VaR: it relies on typical correlation A freedom in stress: define arbitrary comovement What would it mean to stress correlation? Nothing, unless correlation influences performance If measure is P/L: implied correlation is relevant for pricing some derivatives If measure is VaR: correlation affects the estimated percentile.

correlation A freedom in stress: define arbitrary comovement What would it mean to stress correlation?

8 Example 2. Spot-Vol grid P/L for an option depends on 2 risk factors: Underlying Price and Implied Volatility Construct a 2-D grid with range of moves in each risk factor Calculate P/L for each cell in the grid Stress test = worst outcome Stress scenario is portfolio dependent Worst outcome may not be at extreme values of risk factors Issue: full repricing vs. linear approximation Alternative measure: delta or gamma for given scenario

a 2-D grid with range of moves in each risk factor Calculate P/L for each cell in the grid Stress test =

9 Example 3. Using historical scenarios Combination of 3 desks: Bond trading, CDS, and correlation products (tranched CDO) Scenarios based on history of bond spreads, IR, and FX changes during the Bond backup (1994) Estimated P/L: linear approximation using CS01 and DV01 and FX exposure Calculated for each desk for rolling 1-month horizons during the historical period Sum of worst for each is the stress number Historical series automatically include multidimensional risk factor changes Missing risk factors: CDS didn t exist in 1994

history of bond spreads, IR, and FX changes during the Bond backup (1994) Estimated P/L: linear approximation using CS01 and DV01 and

10 Example 4. Hypothetical scenarios Scenarios of changes in multiple risk factors: FX, IR by currency/region, swap and corp spreads, equities Headline event + judgment for impact on markets, e.g. Emerging Mkt crisis, US stock crash, etc. Results tabulated for each line of business, e.g. EM crisis: FX 10MM, IRDeriv 5MM, EqD 25MM for Total 40MM. US crash: FX 2MM, IRD +5MM, EqD +40MM for Total +43MM Gain in a stress scenario? Trading desks may avoid directional risk Scenario may not test actual vulnerabilities Long option positions gain from mkt volatility

event + judgment for impact on markets, e.g. Emerging Mkt crisis, US stock crash, etc. Results tabulated for each line of business, e.g. EM crisis: FX 10MM, IRDeriv 5MM, EqD 25MM for Total 40MM.

11 Example 5. Pricing stress protection Structured equity investment: gives client option-type payoff long put for downside protection and short call giving up some upside. Bank constructs discrete portfolio insurance strategy taking on risk that equity prices drop too fast to perform the necessary rebalancing Extensive risk mitigants and triggers part of the deal so probability of gap risk is beyond 99 th percentile Client pays spread in excess of bank funding costs What s the value of the deal? NPV of excess spread Cost of structuring: tax, legal, deal monitoring Value of gap risk coverage

12 Pricing stress protection (cont.) Construct stochastic process for equity value using stressed parameters, higher volatility, low liquidity Evaluate prob-weighted gap losses via simulation As part of setting up deal: set triggers for rebalancing, cushions - use stress historical parameters As part of valuing gap risk for given deal: calibrate parameters to match observable prices and then apply to deal (risk neutral prob and risk-free discounting) Challenges: Does the history include the stress events? Finding market observables to calibrate Relation between market terms and structure

simulation As part of setting up deal: set triggers for rebalancing, cushions - use stress historical parameters As part of valuing gap risk for

Jornadas Economicas del Banco de Guatemala. Managing Market Risk. Max Silberberg

Jornadas Economicas del Banco de Guatemala. Managing Market Risk. Max Silberberg Managing Market Risk Max Silberberg Defining Market Risk Market risk is exposure to an adverse change in value of financial instrument caused by movements in market variables. Market risk exposures are